Question

Name some algebraic identities

Answer 1

1. (a+b)2 = a2 + 2ab + b2

2. (a-b)2 = a2 - 2ab + b2

3. (a+b) (a-b) = a2 -b2

4. (x + a)(x + b) = x2 + (a + b) x + ab

5. (x + a)(x - b) = x2 + (a - b) x - ab

6. (x - a)(x + b) = x2 + (b - a) x - ab

7. (x - a)(x - b) = x2 - (a + b)x + ab

8. (a + b)3 = a3 + b3 +3ab (a + b)

9. (a - b)3 = a3 - b3 - 3ab (a - b)

10. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz

11. (x + y - z)2 = x2 + y2 + z2 + 2xy - 2yz - 2xz

12. (x - y + z)2 = x2 + y2 + z2 - 2xy - 2yz + 2xz

13. (x - y - z)2 = x2 + y2 + z2 - 2xy + 2yz - 2xz

14. x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz -xz)

15. x2 + y2 = 1212 [(x+y)2 + (x-y)2]

16. (x+a) (x+b) (x+c) = x3+ (a + b + c ) x2 + (ab + bc +ca) x + abc

17. x3 + y3 = (x + y) ( x2 - xy + y2)

18. x3 - y3 = (x - y) ( x2 + xy + y2)

19. x2 + y2 + z2 -xy -yz -zx = 1212 [(x-y)2 + (y -z)2 + (z -x)2]

these are identies.

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Answer 2

1.(a+b)2=a2+2ab+b2

2.(a-b)2=a2-2ab+b2

3.(a2-b2)=(a-b)(a+b)

4.(x+a)(x+b)=x2+(a+b)x+ab

Hope its help you